Macrostructure modeling with microstructure reflectance slices

ABSTRACT

A method and system for efficient synthesis of photorealistic free-form knitwear, where a single cross-section of yarn serves as the basic primitive for modeling entire articles of knitwear. This primitive, called the lumislice, describes radiance from a yarn cross-section based on fine-level interactions, including occlusion, shadowing, and multiple scattering, among yarn fibers. By representing yarn as a sequence of identical but rotated cross-sections, the lumislice can effectively propagate local microstructure over arbitrary stitch patterns and knitwear shapes. This framework accommodates varying levels of detail and capitalizes on hardware-assisted transparency blending. To further enhance realism, a technique for generating soft shadows from yarn is also introduced.

TECHNICAL FIELD

This invention relates generally to three-dimensional (3D) modeling, andmore specifically to modeling of macrostructure objects composed ofelongated fibers, such as knitwear and hairpiece modeling.

BACKGROUND

Textiles and clothing are part of everyday life. As such, realisticrendering of these articles has been an active area of computer graphicsresearch for over a decade. In particular, modeling and rendering ofknitwear poses a considerable challenge. Knitwear is constructed byspinning raw fibers into yarn. The yarn is then knitted into fabricbased on a stitch pattern, and may optionally include a color pattern aswell. The knitted fabric is then sewn into the desired clothing, such asa hat, scarf, or other type of clothing.

One obstacle to realistic knitwear generation is the complicatedmicrostructure of yarn. Close examination of yarn reveals countless thinfibers which give knitwear a fuzzy appearance. In order to be accurate,a computer rendering of a close-up view of knitwear should show fuzzyyarn fibers. Improper rendering of delicate fuzzy yarn fiber structurescan result in aliasing that causes a scene to look artificial. Renderinga down-like covering with existing techniques is inadequate andcumbersome in that its appearance changes in detail with differentviewing distances.

Another difficulty presented by knitwear is its variations in shape. Forknitwear lying flat, its microstructure has been efficiently displayedusing prior art volume-rendering techniques; however, the only knowntechniques for rendering free-form knitwear with microstructure utilizeGouraud-shaded triangles, which was presented by H. Zhong, Y. Xu, B.Guo, and H. Shum, in the publication titled “Realistic and EfficientRendering of Free-Form Knitwear”, published in the Journal ofVisualization and Computer Animation, Special Issue on Cloth Simulation,in February 2001 (Zhong et al.). Techniques disclosed in Zhong et al.,however, do not accurately handle close-up views.

Curved ray tracing, which is computationally expensive, does noteffectively deal with multiple scattering that is especially evident onlight-colored yarn. Curved ray tracing has a high rendering cost, andusers must build different volumetric textures for different knittingpatterns. This makes it difficult to model knitwear with advancedstitching patterns. Also, difficulties arise when the knitwear isseverely deformed.

To avoid the high cost of ray tracing, volumetric objects can berendered by hardware-aided texture mapping with transparency blending.Limitations arise, however, from the use of graphics hardware. Graphicshardware in general cannot compute the shading or shadowing for eachindividual texture pixel, with the exception of the GeForce 3 graphicshardware model that is provided through the NVIDIA Corporation having aplace of business at 2701 San Tomas Expressway, Santa Clara, Calif.95050, and which can do per-pixel lighting but cannot capture multiplescattering nor the attenuation effect of light passing through yarn. Ifa two dimensional (2D) alpha texture is employed, the volumetric texturecan be split into slices parallel to the viewport and sorted from far tonear for accurate blending computation. Splitting and sorting aresolvable, but if shading and shadowing cannot be accurately computedaccording to the lighting and viewing conditions of the volumetrictexture, the rendering result would likely appear artificial. A way toachieve realistic shading effects is to compute the results of allpossible lighting and viewing conditions offline, and save them in avolumetric texture data structure. A moderately complex scene, however,requires a prohibitive amount of storage and computation resources.

Unlike woven fabrics, which can be well represented by specializedbidirectional reflectance (BRDF) models, knitwear is characterized by amacroscopic stitch structure that requires an explicit model of theknitting pattern and geometry. The microstructure of knitted yarntypically consists of a large number of thin fibers, where the size ofyarn and stitches exceeds that of thread, thus precluding representationby BRDF models. Currently there are no convenient techniques forcomprehensive photorealistic synthesis of knitwear.

Photorealistic rendering of a material that is arranged repetitivelyinto a macrostructure poses another problem when fine-level interactionsare apparent among the relatively smaller elements that make up thematerial. Examples of these smaller elements that make up a materialinclude fibers in a yarn that have been knit into knitwear, orindividual hairs that are on a human head. These relatively smallerelements exhibit reflection and transmission interactions, which includeshadowing, occlusion, and multiple scattering, which need to beconsidered for physically realistic rendering. Such details shouldmoreover be visible over the entire object and change in appearance forvarying viewing distances. Additionally, rendering methods shouldaccommodate arbitrary forms of the material. These difficulties togetherhave not been addressed by previous rendering approaches so as toachieve photorealistic rendering of knitwear that efficiently handlesfree-form surfaces, varying levels of detail from different viewingdistances, and complex stitch geometry.

SUMMARY

A computer rendering system and method are presented for moving a planarplurality of reflection points perpendicular with respect to an axis torender an image of the plurality of reflection points at a plurality ofpositions with respect to the axis. Also presented are a system andmethod for rendering a macrostructure having a repetitivemicrostructure. Examples of such a macrostructure are knitwear, hair,carpets, and weaves. The repetitive microstructures are defined hereinin terms of reflectance slices or “lumislices”. A reflectance slice orlumislice is a basic primitive for photorealistic rendering of suchmacrostructures. The lumislice, which represents a typical cross-sectionof a material of which an object is composed, represents light radiancefrom a yarn cross-section. Based upon the repetitive structure of yarn,articles of knitwear may be composed of lumislices.

Implementations of the system and method account for light reflectionand transmission details by modeling the entire object as a collectionof lumislices. A lumislice models the fine-level light reflections andtransmissions among the to-be-rendered material's individual elements.The lumislice can then be swept along the material that makes up theobject to be rendered to produce photo-realistic renderings. Thelumislice effectively propagates the material's local microstructureover the entire object to produce photorealistic renderings thataccommodate varying levels of detail. As the lumislice represents amicrostructure element of the larger material that makes up the object,the lumislice has the flexibility to be incorporated into any globalshape. The lumislice, as a semi-transparent texture slice, can be usedto render fuzzy objects such as animal hair, e.g. fur, as well as humanhair via sweeping the object with the lumislice and then rendering aresultant sampled collection of lumislices.

BRIEF DESCRIPTION OF THE DRAWINGS

Generally, the same numbers are used throughout the drawings toreference like elements and features.

FIG. 1 is a computer rendering of a nonplanar or free form parameterizedsurface.

FIG. 2 is a computer rendering of linked control points that have beendetermined for the shape of the free-form parameterized surface seen inFIG. 6.

FIG. 3 is a computer rendering of the free-form surface with controlpoints seen in FIG. 2, where the elongated strands connecting thecontrol points have a stitching pattern placed there over so as to forma knitwear skeleton.

FIG. 4 is a top planar view rendering showing the two dimensionalappearance of a lumislice, and particularly showing a plurality ofpoints in varied density.

FIG. 5 is a perspective view on the left of a computer rendering of theappearance of a single lumislice, where the perspective view on theright shows a sampling of the lumislice that has been rotated andtranslated along an axis.

FIG. 6 is a computer rendering of a knitted fabric after the lumislicesampling of FIG. 4 has been swept and rotated along the paths of thestitching pattern of the knitwear skeleton seen in FIG. 3, and to whichsoft shadows have been added.

FIGS. 7 a-7 d are, respectively, farther distance computer renderings ofknitwear fabric that has been synthesized using the lumislice.

FIGS. 8 a and 8 b are perspective views of a computer rendering showinga single lumislice on the left and a sampling of lumislices on the rightthat have been rotated and translated along an axis.

FIGS. 9 a-9 c are computer renderings, where FIG. 9 a is planar view ofa lumislice, FIG. 9 b is a sample of three (3) of the lumislice of FIG.9 a in perspective view, and FIG. 9 c is sweeping sampling of thelumislice of FIG. 9 a along and about an axis.

FIGS. 10 a-10 c depict partitioning of lumislices for transparencyblending.

FIGS. 11 a and 11 b illustrate, respectively, a lumislice and its plotfor transmission of light for soft shadows.

FIGS. 12 a-12 b characterize representations of levels of resolution ofknitwear rendered using a lumislice implementation.

FIG. 13 is a block diagram of a system architecture for rendering amacrostructure knitwear object from microstructure lumislice primitives.

FIG. 14 is a flow chart depicting actions for an implementation of amethod for rendering a scene of a macrostructure knitwear object withmicrostructure lumislice primitives.

FIGS. 15 a and 15 b are computer renderings of a knitwear hat and scarfwithout and with shadows, respectively.

FIGS. 16 a-16 d are computer renderings using a lumislice implementationof a range of complex stitching patterns that include soft shadows.

FIG. 17 is an illustrative example of a computing operating environmentcapable of implementing, either wholly or partially, a lumislicealgorithm.

DETAILED DESCRIPTION

Implementations of the present invention employ a microstructure elementto render a macrostructure object. In one implementation, knitwear is amacrostructure object and the microstructure element is a reflectanceprimitive for yarn that represents a microstructure in a manner thatallows for various levels of detail and hardware-assisted rendering.

Although patterns of knitted yarn in knitwear can be complex, they arecomposed of a single basic element. For a given type of yarn, thedistribution of fibers for each cross-section or slice is similar. Animplementation to render knitwear models a yarn strand by winding afixed two dimensional (2D) fluff distribution along the path of the yarnso as to synthesize knitwear from a single volumetric yarncross-section. To exhibit realism, this cross-section incorporates finevisual effects, such as self-occlusion, self-shadowing, and multiplescattering. For different levels of detail, the resolution of this slicecan be varied with smooth visual transitions. The slice is compactlyrepresented in 2D as a single thin volumetric layer and can be computedoffline. In addition, this structure is amenable to transparencyblending for efficient rendering.

1. Lumislice-Based Rendering

Implementations of the invention directed to knitwear generated from alumislice include both modeling and rendering. With respect to modeling,two components are included which are a lumislice and a stitch skeleton.FIGS. 1-6 provide an overview of the rendering process through thedepiction of the geometric construction of a knitwear article.

1.1 Object Synthesis

FIGS. 1-3 a depict the geometric construction of a knitwear article. Forthe desired free form, or nonplanar, parameterized surface shown in FIG.1, the shape of the knitwear is defined by control points as seen placedin FIG. 2. Each control point is connected to other control points by aplurality of axes. The defined control points are also used to outlinestitch patterns, such that the control points are fit with a chosenstitching pattern, as seen in FIG. 3 a, thereby delineating a knitwearskeleton. As such, the knitwear skeleton defines the yarn path.

The knitwear skeleton seen in FIG. 3 a is a macrostructure that isgenerated by an implementation of the invention. The macrostructureeffectively defines a 3D surface with the control points, each being atan intersection of two of the axes. The 3D surface can be furtherpartitioned into quadrilaterals in accordance with the object to bemodeled and corresponding to the stitch pattern. An example of thispartitioning is seen in FIG. 3 b where a quadrilateral 318 is seen andabout which a stitch pattern 300 is defined. Quadrilateral 318, which isintended to be represented upon a 3D surface, connects several keypoints of stitch pattern 300. Each key point of stitch pattern 300occurs at a control point. Several of the key points serve as a terminalend for a curved segment of stitch pattern 300.

In stitch pattern 300 of FIG. 3 b, quadrilateral 318 has a correspondingstitch 302. Stitch 302 is defined by curved segments connecting the sixkey points of the stitch 302. The point 304 is a key point of the stitchimmediately to the left of the stitch 302, which is not specificallycalled out in FIG. 3 b. Connecting the point 306 with the point 304connects the stitch 302 with another stitch.

The key points of all of the quadrilaterals determine the overall shapeof the knitwear model. Since the control points have respective physicalrelationships, so do the key points. As such, the relations among allthe key points preserve the knitwear topological connections duringstretching and deformation. As the underlying surface changes shape,each stitch loop also changes shape depending on its location in theknitwear. At the same time, each loop remains correctly interlocked withneighboring loops.

Both a color pattern and a stitch pattern can be applied to thethree-dimensional surface of the macrostructure in accordance with theknitwear skeleton seen in FIGS. 3 a and 3 b. In this case, eachquadrilateral 318 of stitch pattern 300 would have a color from thecolor pattern applied thereto. The application of a color from a colorpattern is optional and the knitwear upon the knitwear skeleton can berendered to be monochromatic.

A variety of techniques, other than that disclosed herein, can be usedto define the stitch and color patterns of the macrostructure thatdefines an article of knitwear. One such technique, discussed above, isthat of Zhong et al.

The knitwear's reflectance properties are determined from FIGS. 4-5. InFIG. 4, a cross-sectional fluff density distribution is shown as avisual representation of a lumislice. The appearance of the lumislice isas several clusters of points, or fluff, in a two dimensional (2D) areaor plane. The density of the points is seen to vary over the 2D plane.The computation of the lumislice is to be used as the basic structuralprimitive for an entire piece of knitwear. This computation is made byfirst measuring or choosing a density distribution of the yarn fibersseen in FIG. 4, and then computing the lumislice. The knitwear skeletonseen in FIG. 3 is divided into yarn segments. The reflectancecharacteristics of these yarn cross-sections are each represented by thelumislice, which is then stored in a lookup table of 2D transparencytexture. The yarn segments are further divided into volumetric slices asseen in FIG. 5. The volumetric slices are then rendered according tolumislice lighting and viewing conditions using hardware-aidedtransparency-blending application program interfaces (APIs). Thevolumetric lumislices seen in FIG. 5 are swept and rotated along thepaths of the knitwear skeleton seen in FIG. 3 to form the largenonplanar knitwear fabric seen in FIG. 6. Soft shadows can optionally beadded, as in FIG. 6, for greater realism.

1.2 The Lumislice

The lumislice represents radiance from a yarn cross-section and arisesfrom an observation that, based on the repetitive structure of yarn,articles of knitwear may be composed entirely of lumislices. Thissuggests a local and global structural hierarchy that can be formed foryarn to facilitate efficient photorealistic rendering. On the localhierarchy, there will be fine-level interactions among yarn fibers thatinclude occlusion, shadowing, and multiple scattering. The results oftheir reflectance interactions, which can be modeled for a yarncross-section, when so modeled are called a ‘lumislice’. An assumptioncan be made that the fluff on all cross-sections that are to be renderedfollow the same fluff density distribution. On the global hierarchy,because of the repetitive nature of knitted yarn and its known pathalong a skeleton, knitwear can be represented as a collection ofidentical lumislices in various positions and orientations. It is thisdetailed but flexible quality that gives the lumislice much utility.Local microstructure can be closely represented in the lumislice, yet itcan be globally disseminated to all points of a knitwear in that it doesnot introduce restrictions on the global structure of the knitted yarn.

Enhanced realism can be achieved with a shadow map presented herein foryarn that is integrated into an implementation for soft shadowgeneration. Inclusion of such shadows can allow individual yarn fibersto be distinguished, as deep shadow maps have done for hair.

Examples of lumislice-based renderings of a knitted fabric are seen inFIGS. 7 a and 7 b for different viewing distances, where FIGS. 7 a isthe closest view and FIG. 7 d is the furthest view. The closest view inFIG. 7 a exhibits the delicate fluff and fuzzy characteristics ofknitted yarn. FIG. 7 a depicts a section that is taken from the fartheraway view of FIG. 7 b. FIG. 7 c is a section of the still farther awayview in FIG. 7 d that is a rendering of variable macrostructure thatparticularly illustrates irregular stitches. The efficient and effectivegeneration of this range of details distinguishes lumislice-basedrendering.

The lumislice may furthermore be extended to other materials that aremade up of subpixel elements, such as hair, carpet or distant foliage.Applications of photorealistic knitwear rendering include web-baseddisplay of clothing products and fabric animation on moving characters.Automated generation of knitwear would also be desirable for motionpictures depicting anthropomorphized clothed furry animals, where furand clothing structures would otherwise require significant labor to besynthesized.

FIGS. 8 a-8 c and 9 a-9 b shows a perspective view of a lumislice thathas been sampled while it is rotated about and translated relative to anaxis ‘t’. It can be seen in FIGS. 8 c, 9 a, and 9 b that the combinedsampled lumislices give each point on the 2D plane the appearance of anelongated strand or fiber. FIG. 8 b shows an example of three (3)periodic samples of a lumislice that are taken while rotating about andtranslating along axis ‘t’. When periodic samples of the lumislice aretaken as the lumislice is rotated about axis ‘t’ while being translatedalong axis ‘t’, FIGS. 8 c, 9 a, and 9 b show that the combination ofsampled lumislices assumes the appearance of multiple fibers in a yarn.Yarn so rendered can be arranged into geometric, repetitive shapes, suchas stitches so as to form a larger knitwear fabric, as seen in FIG. 6.The knitwear fabric seen in FIG. 6 can then be used in a computerrendering over a non-planar free form surface for a physically basedanimation, such as the knitwear cap and scarf seen in FIGS. 15 a-15 b,which may be formed by lumislices swept along the various paths ofcomplex stitching as is seen in FIGS. 16 a-16 d. The technique for thepresented renderings will now be discussed.

The Lumislice Computation

The lumislice is the fundamental structure implemented for knitwearrendering. Attributes of the lumislice facilitate the rendering ofknitwear at different viewing distances while maintaining appropriatemacrostructure and macrostructure features. For a given illuminationdirection, the lumislice is computed as a light field for a yarncross-section. The lumislice characterizes attributes of across-sectional slice of yarn that is divided into voxels.

Each lumislice voxel has two associated quantities. The first quantityof each lumislice voxel is the opacity value of its yarn fluff, which isa value derived from the fluff density distribution of the yarn fibersas illustrated in FIG. 9 a, and assumes that each lumislice voxel isuniform for all cross-sections of the given yarn. For yarns withdifferent fluff characteristics, its corresponding density distributionsare used instead. The second quantity is a shading or Volume ReflectanceFunction (VRF), which represents the exhibited brightness of the voxelwhen viewed and illuminated from various directions. The density valuescan be measured from a representative cross-section of yarn, and theVRFs are computed from these densities using an emission-absorptionmodel for volume illumination by sampling different viewing and lightingdirections.

Each of these voxels has an associated four-dimensional array thatcontains its opacity and its voxel reflectance function (VRF). The VRFrepresents the brightness of a voxel viewed from directionV(θ_(v),φ_(v)), seen in FIG. 9 b, when illuminated by a unit intensitylight from direction L(θ_(l),φ_(l)). The VRF differs from thetraditional notion of a bidirectional reflectance function (BRDF) inthat it accounts for the attenuation of incident light passing throughthe surrounding yarn. Using the VRF allows the precomputation of theeffects of the surrounding yarn. A cross-section of one yarn, as shownin FIG. 9 a, is composed of lumislice voxels.

Different kinds of yarn can be incorporated into a lumisliceimplementation by employing different cross-sectional fiber densitydistributions. Additionally, multiple scattering is calculatediteratively from reflections among neighboring voxels. The lumislice isprecomputed and stored in tables such that hardware-assistedtransparency blending can accelerate the rendering. Differentresolutions of precomputed lumislices can be displayed depending uponthe various levels of detail that arise from viewing a knitwear articlefrom different distances.

The single computed lumislice could be used for generating entirestrings of yarn as exhibited in FIG. 9 b. Simply by rotating thelumislice along the path of a yarn, arbitrary segments can besynthesized. It should be noted that all lumislices that comprise theyarn are identical in structure and that the yarn can follow any desiredpath. In this way, the fine-level reflectance details of yarn that arecaptured within the lumislice can easily be spread over an entirearticle of knitwear, and there are no restrictions on the shape of theknitwear.

An implementation of the VRF is presented in terms of R_(p), theoutgoing radiance from voxel p. Three primary physical elements factorinto the reflectance at a voxel p: the fluff density ρ_(p), the shadingmodel ψ of yarn, and the incident light distribution I_(msp) thatresults from multiple scattering among neighboring voxels N. Theemission intensity from a voxel in principle can also affect a VRF, butthis quantity for yarn is zero. These factors influence R_(p) accordingto $\begin{matrix}{{R_{p} = {\rho_{p}{\psi\left( {I_{p} + {I_{L}{\sum\limits_{N}\quad I_{msp}}}} \right)}}},} & (1)\end{matrix}$where I_(L) is the light intensity and I_(p) is its attenuated intensityupon reaching p, as shown in FIGS. 9 a and 9 b. A shading model ψ fordiffuse reflection is used, and multiple scattering will be lateraddressed. An emission-absorption model of volume illumination, I_(p),may be expressed as $\begin{matrix}{{I_{p} = {I_{L}{\mathbb{e}}^{{- \gamma}{\sum\limits_{r = p}^{P_{i\quad n}}\quad\rho_{r}}}}},} & (2)\end{matrix}$where P_(in) is the point of light entry into the yarn bounding box, γis a light transmission factor in the emission-absorption model, andvoxel dimensions are unit length. Then Eq. (2) can be substituted intoEq. 1 to produce $\begin{matrix}{R_{p} = {\rho_{p}\psi\quad{{I_{L}\left( {{\mathbb{e}}^{{- \gamma}{\sum\limits_{r = p}^{P_{i\quad n}}\quad\rho_{r}}} + {\sum\limits_{N}\quad I_{msp}}} \right)}.}}} & (3)\end{matrix}$

R_(p) can then be restated in terms of the spherical angles in FIG. 4:R _(p)(θ_(l),φ_(l),θ_(v),φ_(v))=I _(L) C_(p)(θ_(l),φ_(l),θ_(v),φ_(v)),  (4)where $\begin{matrix}{{C_{p}\left( {\theta_{l},\phi_{l},\theta_{v},\phi_{v}} \right)} = {\rho_{p}{{{\psi\left( {\theta_{l},\phi_{l},\theta_{v},\phi_{v}} \right)}\left\lbrack {{\mathbb{e}}^{{- \gamma}{\sum\limits_{r = p}^{P_{i\quad n}}\quad\rho_{r}}} + {\sum\limits_{i \in N}\quad{I_{msp}\left( {\theta_{i},\phi_{i}} \right)}}} \right\rbrack}.}}} & (5)\end{matrix}$

Here, C_(p) is the VRF, which is a 4D function ofθ_(l),φ_(l),θ_(v),φ_(v). It can be approximately represented by a 4Dcolor array after discretization of the four angles, where thediscretization increments are determined by the accuracy required. Forall lumislices used in one implementation, the longitude angle θε[0,2π]and altitude angle φ_(l)ε[−π/2,π/2] are discretized into 32×21directions, such that the 2D lumislice is computed from a 3D sweptrotation of yarn cross-sections. In normal situations, the distancebetween the knitwear and the light source greatly exceeds the radius ofthe knitted yarn, so the assumption of parallel illumination is made.The spacing of the lumislices along yarn segments is related to theresolution of the lumislice, which is presented in Subsection 1.2.4.4,titled “Level of Detail”. For greater realism, multiple scatteringbetween voxels is calculated to simulate light scattering among thefibers. This effect is quantified in the I_(msp) term, which aggregatesthe reflected intensity from neighboring voxels. For a neighboring voxelN from direction (θ_(i),φ_(i)) its contribution to the multiplescattering towards p is computed from Eq. 4 as $\begin{matrix}{{I_{msp}\left( {\theta_{i},\phi_{i}} \right)} = {\rho_{N}{\psi\left( {\theta_{l},\phi_{l},{- \theta_{i}},{- \phi_{i}}} \right)}{{\mathbb{e}}^{{- \gamma}{\sum\limits_{r = N}^{P_{i\quad n}}\quad\rho_{r}}}.}}} & (6)\end{matrix}$

Although multiple scattering could be computed iteratively from thesurrounding voxels, a first-order approximation with adjacent voxels isadequate. The effect of the multiple scattering component on yarnrendering is visually beneficial for achieving realistic renderings.

For additional simplification, the specular component of the VRF isignored in one implementation, resulting in a view-independentreflectance function. This allows C_(p) to become a 2D function, andconsequently the computational costs and storage requirement aresignificantly reduced. All implementation of lumislices in this oneimplementation consider only the diffuse effect.

The lumislice of a given yarn is precomputed and stored in tables, withthe VRF in a 2D Red-Green-Blue (RGB) color table indexed by(θ_(L),φ_(L)) and the opacity in an alpha table.

1.2.2 Volumetric Yarn and Radiance Calculation

Since the same lumislice, as seen in FIG. 8 a, represents allcross-sections of a knitted yarn, it is rotated and translated along theyarn path to form the yarn volume, as shown in FIGS. 8 c, 9 a, and 9 b.The radiance R of the knitwear at a given image pixel from a viewpointcan be computed as $\begin{matrix}{{R = {\sum\limits_{p = P_{near}}^{P_{far}}\quad{{\mathbb{e}}^{{- \gamma}{\sum\limits_{s = P_{near}}^{p}\quad\rho_{s}}} \cdot R_{p}}}},} & (7)\end{matrix}$where R_(p) is calculated in Eq. 1.

When the knitwear is rendered, all yarn segments are subdivided into aseries of volumetric cross-sections, each represented by the lumislice.When a slice is drawn, its location, its local coordinate system<t,u,v>, the light source position and the viewpoint together determinethe reflection angles θ_(L),φ_(L),θ_(v),φ_(v), as shown in FIG. 9 b.These angles, specifically only θ_(L),φ_(L), are then used to index the2D color table of the lumislice. This color texture and the opacitytable of the slice together form the Red-Green-Blue-Alpha (RGBA)transparency texture, which is rendered by the texture mapping andtransparency-blending functions of standard graphics APIs.

1.2.3 Pattern Stitching

The path of the yarn, and likewise the arrangement of the lumislices, isgiven by the process of pattern stitching. In pattern stitching, aknitwear skeleton is built according to a given object surface andstitch pattern. This method is detailed in Zhong et al. and is brieflydescribed here. The knitwear skeleton is a network of interlockingmathematical curves in three dimensions (3D) which interpolate controlpoints that are placed according to the desired stitch pattern.

An important feature of control points is that they simplify modellingand editing of advanced stitch patterns. An additional advantage of thisframework is the modeling of interactions among yarn loops. Thisfree-form structure for knitwear complements implementations of thelumislice method for realistic and efficient rendering.

1.2.4 Rendering

With stitching, the knitwear skeleton is created on a free-form surface.The yarn along the skeleton is divided into a series of short,discretized straight segments with a twisting angle θ. The frame <t,n,b>is then defined for determining a local coordinate system <t,u,v> foreach slice.

With these slices, the rendering issues of depth sorting, slicepartitioning, shadow casting, and levels of detail are described.Subsections 1.2.4.5-1.2.4.6 describe an implementation of a renderingsystem architecture and algorithm.

1.2.4.1 Sorting Discretized Yarn Segments

For the blending computation, the volumetric yarn slices must be drawnfrom far to near, thus requiring slice sorting before rendering. Whilethe number of slices can be extremely large for complex scenes,implementations involve sorting the yarn segments rather than the slicesif the yarn segments are short. The view direction and the positioningof a yarn segment determine the orientation in which its slices arerendered.

1.2.4.2 Slice Partitioning

The transparency-blending function supported by graphics hardwareperforms its blending computation along slices parallel to the viewport.For knitwear, lumislices can have various orientations that differgreatly from that of the viewport. FIGS. 10 a-10 c illustratepartitioning of lumislices for transparency blending for animplementation, where each figure shows a slice on the left, a viewpointdirection arrow perpendicular to the screen, and top and bottom slicesof different orientation relative to the respective screen in eachfigure.

In FIG. 10 a, for the top and bottom slices with the same transparencytexture, differences in orientation do not lead to different blendingresults if there is no slice partitioning parallel to the image plane.The two slices can have the same blending result even when they arealigned differently and consequently have different thicknesses withrespect to the viewer. This disparity in thickness should in principlebe rendered dissimilarly for semi-transparent surfaces.

In FIG. 10 b, where the lower slice is partitioned according to aparticular resolution, the blending result reflects the difference inthe thickness between the two surfaces as seen from the screen. As such,FIG. 10 b illustrates an approximate solution to the problem of FIG.10A, where an implementation partitions each slice according to itsresolution. Each of the resulting slice units is then rendered as aline, because polygons are taken to have zero thickness by the hardware.This would lead to slices not being rendered when they are perpendicularto the viewport.

In FIG. 10 c, because of hardware discretization of the scene withregards to the viewport pixels, more than one voxel may map to the samescreen pixel. The result would effectively be rendered as shown in FIG.10 c, where there may be more than one line projected to each pixel.

1.2.4.3 Shadows

Shadows, for which there are many well-known generation techniques, areone of the most important factors for realism. Shadows are particularlyimportant for realistic rendering of knitwear because they not onlyindicate the spatial relationship between knitwear and other geometricobjects, but also visually reveal the knitting pattern of yarns. Therendering of FIG. 15 a that lacks shadows, when compared to therendering of FIG. 15 b that implements a shadow generation algorithm,exemplifies the significant effects of shadows on the rendered hat andscarf.

Deep shadow maps can deal with semi-transparent or sub-pixel objectssuch as hair, fur and smoke because they represent the fractionalvisibility through a pixel at all possible depths, rather than only asingle depth value. This technique, however, can be incompatible withimplementations of the lumislice because part of the light attenuationhas been already computed and stored in the lumislice to provide bettereffects of yarn microstructure. The traditional shadow map is thereforeextended to handle yarn, an object having a geometry that is not clearlydefined. While shadows are important in 3D rendering, they need not beexact. As such, lumislice implementations use a rough shadowingtechnique that include two steps.

Like traditional shadow map techniques, the first step places a cameraat the light source, making sure that all shadow generators andreceivers are within the field of view. All objects except for knitwearare then projected to produce a shadow map containing a depth value. Forknitwear, only the centerlines of yarns are projected to the shadow map.Thus the shadow map in one implementation will contain depth informationof geometric objects and yarn centers.

Next, referring to FIGS. 11 a-11 b, the effect range R_(y) of yarn inthe shadow map is computed according to the radius of yarn. Thisparameter is used to determine whether light is partially absorbed bythe yarn before reaching more distant positions.

Finally, before a point p is rendered, it is projected onto the shadowmap for shadow testing. If the projection resultp_(s)(x_(s),y_(s),z_(s)) indicates total occlusion by geometricsurfaces, then it is in shadow. Otherwise, the yarn-occlusion test isperformed as follows: on the shadow map, if the closest distance d from(x_(s),y_(s)) to the centerline of any yarn is smaller than R_(y), lightis partially absorbed by that yarn. Given the fluff density distributionseen in FIG. 11 a, which may be represented as ‘ρ’, the lighttransmission for distance d through voxels (d, i) of the lumislice iscomputed as $\begin{matrix}{{T_{y}(d)} = {1 - {k_{0}\quad\frac{1 - {\prod\limits_{i = {- R_{y}}}^{R_{y}}{\mathbb{e}}^{- {{\gamma\rho}{({d,i})}}}}}{1 - {\prod\limits_{i = {- R_{y}}}^{R_{y}}{\mathbb{e}}^{- {{\gamma\rho}{({0,i})}}}}}}}} & (8)\end{matrix}$where k₀=0.8 and the voxel dimensions are empirically taken to be unitlength.

Implementations of the lumislice-based method render knitwear by avolumetric yarn slice using hardware-aided transparency blending.Shadows cannot be calculated for every pixel on a texture if thealpha-texture is employed to render volume-represented objects. Thus theshadow test can be performed only at the slice vertices, and the resultis blended to the lumislice by adjusting the texture brightness so thatthe shadow effect can be seen. If higher accuracy is required, such asfor rendering close-up views, the slice could be divided into sub-slicesso that shadow computation can be done at more points to improve theresult quality.

1.2.4.4 Level of Detail Representation

To handle a wide range of viewing distances, a view-dependent level ofdetail representation of the lumislice is utilized to reduce thecomputational cost, to ensure smooth visual transitions, and to reducerendering error. When the viewing distance changes, the projection sizeand visible features of a yarn slice on the screen should changeaccordingly. A lumislice of fixed resolution can cause errors when thereis no simple method for determining proper opacity values, even thoughthe color values of the lumislice can be obtained by using a mip-map.For this reason, lumislices of different resolutions can be precomputed.Then, a rendering can be made of each precomputed slice that is the mostappropriate for its current viewing condition.

For decreasing resolution of the lumislice, the lumislice unit ofthickness should increase by the same factor. For instance, alow-resolution lumislice can be formed as the composite of two identicalhigh-resolution lumislices. FIGS. 12 a-12 b depict lumislice levels ofdetail. To form the lower resolution lumislice of FIG. 12 b, ahigh-resolution lumislice is doubled in thickness as of FIG. 12 a, andthen groups of eight (8) voxels are averaged according to Eq. 9 asfollows. Locally, a voxel on a low-resolution slice can be computed fromcorresponding voxels in a high-resolution slice. A reasonable estimateof the low-resolution density ρ′ is its average value, and a reasonableestimate of the color C′ is a weighted average, as follows:$\begin{matrix}{{\rho^{\prime} = {\frac{\rho_{1} + \rho_{2} + \rho_{3} + \rho_{4} + \rho_{5} + \rho_{6} + \rho_{7} + \rho_{8}}{8}\quad{and}}}{C^{\prime} = \frac{{C_{1}\rho_{1}} + {C_{2}\rho_{2}} + {C_{3}\rho_{3}} + {C_{4}\rho_{4}} + {C_{5}\rho_{5}} + {C_{6}\rho_{6}} + {C_{7}\rho_{7}} + {C_{8}\rho_{8}}}{\rho_{1} + \rho_{2} + \rho_{3} + \rho_{4} + \rho_{5} + \rho_{6} + \rho_{7} + \rho_{8}}}} & (9)\end{matrix}$where C₁, C₂, C₃, C₄, C₅, C₆, C₇, C₈ are colors of the high-resolutionslice, and ρ₁,ρ₂,ρ₃,ρ₄, ρ₅,ρ₆,ρ₇,ρ₈ are densities of the high-resolutionslice, Because of thickness doubling, the estimate of the transparencyis T′=(e^(−γρ′))². For more accurate results when the resolution isbelow 8×8, the low-resolution lumislice can be formed by sampling thehigh-resolution lumislice.

The resolution for rendering a slice depends upon the projection area ofthe slice on the screen. For a projection whose dimensions are at themost m pixels, a lumislice with resolution 2n×2n is chosen such that nis an integer and 2^(n)≧m, to prevent aliasing. Although thisimplementation precomputes lumislices at intervals according to 2^(n),finer intervals may be implemented for more accuracy.

The unit length corresponding to the determined resolution alsodescribes the thickness of the lumislice. Lumislice densities along yarnare determined by dividing yarn segments by these computed resolutionunits. In other words, if the lumislices are considered to betwo-dimensional, the resolution unit describes the distance betweenlumislices along yarn segments.

1.2.4.5 Rendering System Architecture

FIG. 13 is a block diagram of an implementation of a lumislice systemarchitecture 1300. The exterior components outside of the lumislicesystem architecture 1300 represent inputs (1302, 1306, 1312, 1314, 1316,1326, 1328, 1320) to the lumislice system architecture 1300, with thesynthesized scene 1338 as the output from the lumislice systemarchitecture 1300. From a parameterized surface describing the desiredknitwear shape that is input to the lumislice system architecture 1300at Action 1302, control points for the shape are determined at Action1304. An example of a parameterized surface is seen in FIG. 2 a, and anexample of control points connected by axes is seen in FIG. 2 b.Knitting and color patterns are input to the lumislice systemarchitecture 1300 at Action 1306, which are placed along the controlpoints determined at Action 1304 to form a skeleton of the yarn stitchesat Action 1308. An example of a yarn stitch skeleton is seen in FIG. 2c. The yarn stitch skeleton determined at Action 1308 is thendiscretized into yarn segments at Action 1310. For a given viewingcondition, the yarn segments from Action 1310 are sorted by distancefrom the viewer at Action 1320. The unsorted yarn segments from Action1310 are also used with the scene geometry input at Action 1314 and alsowith a lighting condition input at Action 1316 to compute the shadow mapof the scene at Action 1324 as described above in Subsection 1.1.2.4.3.A lumislice is computed at Action 1324 from several inputs, includingthe fiber distribution of the yarn cross-section that is input at Action1326, as well as the slice resolution and the sampling density for thelumislice which are respectively input to the lumislice systemarchitecture 1300 at Actions 1328 and 1330. The shadow map computed atAction 1324, the yarn segments sorted at Action 1320, and the conditionsof viewing and lighting input at Actions 1314, 1316 are used along withthe lumislice computed at Action 1324 for rendering the synthesizedscene of the knitwear at Action 1338. An example of the renderedknitwear is seen in FIGS. 6, 15 a, 15 b, and 16 a-16 d.

1.2.4.6 Rendering Algorithm

From the implementations described above, actions to implement arendering algorithm are presented in this Subsection 1.2.4.5, whereinthe given models of the lumislice and the knitwear skeleton are used.

FIG. 14 depicts an implementation of a rendering routine 1400. Renderingroutine 1400 includes an Action 1402 that creates a shadow map. Theprocess to create a shadow map is as described in Subsection 1.2.4.3,above. At Action 1404, an ID color method is used to draw the color anddepth of geometric objects as seen from the viewport into a 1^(st) ImageBuffer. In Action 1406, the result of the geometric objects in the1^(st) Image Buffer is drawn as cylindrical polygons. The resultingimage in the 1^(st) Image Buffer is then converted into a bitmap. Pixelsthat are covered by yarn are set to 0, and others are set to 1.

At Action 1408, geometric objects are drawn with the shadow test underthe same projection condition. The result is then saved in a 2^(nd)Image Buffer. Yarn segments that were discretized at Action 1310 of FIG.13 are then sorted by depth or distance from the viewpoint at Actions1320, 1410, respectively, of FIGS. 13 and 14. At Action 1412, the depthtest is disabled. The use of hardware-aided graphics APIs entails themasking or disabling of the z-buffer depth test for accuratetransparency-blending computation. Consequently, the rendering of ascene in this implementation can require more than one action. Afterthis disabling of the z-buffer depth test, the volumetric yarn is drawnon the result of Action 1408.

Before each slice is rendered, the vertices of each slice are projectedinto the 1^(st) Image Buffer. If the slice is totally occluded bygeometric objects, the slice is not rendered. Then all slices of theyarn segments are rendered going from the far slices to the near slices.The results is then saved in the 3^(rd) Image Buffer at Action 1412.

For every pixel in the 3^(rd) Image Buffer, a check is made as to itscorresponding value in the 1^(st) Image Buffer at Action 1414. If thevalue is 1, then the pixel should display a geometric object, so thecolor of this pixel is replaced by the color of the corresponding pixelin the 2^(nd) Image Buffer so as to properly process slices that arepartially occluded. The final result is obtained after all the pixelsare checked. The scene can then be synthesized, as in Action 1338 ofFIG. 13.

From the summary, those of skill in the art of textile modeling willappreciate that lumislice-based implementations for knitwear modelinghave the following advantages:

-   -   fine-level interaction among yarn fibers can be precomputed and        used throughout a piece of knitwear;    -   different levels of detail for varying viewing distances are        handled by multiresolution lumislices, in a manner similar to        mip-maps;    -   a knitwear skeleton can be created on a free-form surface, which        facilitates physically based animation and other applications;    -   the lumislice can be used for rendering arbitrary stitch        patterns with better visual effects and lower cost than ray        tracing. Existing volumetric representation methods have        significant difficulties in dealing with complex stitches on a        deformable surface; and    -   implementations of the lumislice can be implemented by standard        graphics application program interfaces (APIs), such as Open        Graphics Language (OpenGL).

Exemplary Computing System and Environment

FIG. 17 illustrates an example of a suitable computing environment 1700within which the macrostructure modeling with microstructure reflectanceslices system and method, as described herein, may be implemented(either fully or partially). The computing environment 1700 may beutilized in the computer and network architectures described herein.

The exemplary computing environment 1700 is only one example of acomputing environment and is not intended to suggest any limitation asto the scope of use or functionality of the computer and networkarchitectures. Neither should the computing environment 1700 beinterpreted as having any dependency or requirement relating to any oneor combination of components illustrated in the exemplary computingenvironment 1700.

The macrostructure modeling with microstructure reflectance slicessystem and method may be implemented with numerous other general purposeor special purpose computing system environments or configurations.Examples of well known computing systems, environments, and/orconfigurations that may be suitable for use include, but are not limitedto, personal computers, server computers, thin clients, thick clients,hand-held or laptop devices, multiprocessor systems,microprocessor-based systems, set top boxes, programmable consumerelectronics, network PCs, minicomputers, mainframe computers,distributed computing environments that include any of the above systemsor devices, and the like.

The macrostructure modeling with microstructure reflectance slicessystem and method may be described in the general context ofcomputer-executable instructions, such as program modules, beingexecuted by a computer. Generally, program modules include routines,programs, objects, components, data structures, etc. that performparticular tasks or implement particular abstract data types. Themacrostructure modeling with microstructure reflectance slices systemand method may also be practiced in distributed computing environmentswhere tasks are performed by remote processing devices that are linkedthrough a communications network. In a distributed computingenvironment, program modules may be located in both local and remotecomputer storage media including memory storage devices.

The computing environment 1700 includes a general-purpose computingdevice in the form of a computer 802. The components of computer 1702can include, but are not limited to, one or more processors orprocessing units 1704, a system memory 1706, and a system bus 1708 thatcouples various system components including the processor 1704 to thesystem memory 1706.

The system bus 908 represents one or more of any of several types of busstructures, including a memory bus or memory controller, a peripheralbus, an accelerated graphics port, and a processor or local bus usingany of a variety of bus architectures. By way of example, sucharchitectures can include an Industry Standard Architecture (ISA) bus, aMicro Channel Architecture (MCA) bus, an Enhanced ISA (EISA) bus, aVideo Electronics Standards Association (VESA) local bus, and aPeripheral Component Interconnects (PCI) bus also known as a Mezzaninebus.

Computer 1702 typically includes a variety of computer readable media.Such media can be any available media that is accessible by computer1702 and includes both volatile and non-volatile media, removable andnon-removable media.

The system memory 1706 includes computer readable media in the form ofvolatile memory, such as random access memory (RAM) 1710, and/ornon-volatile memory, such as read only memory (ROM) 1712. A basicinput/output system (BIOS) 1714, containing the basic routines that helpto transfer information between elements within computer 1702, such asduring start-up, is stored in ROM 1712. RAM 1710 typically contains dataand/or program modules that are immediately accessible to and/orpresently operated on by the processing unit 1704. System memory 1706 isan example of a means for storing data having inputs and outputs and aframe buffer for storing pixel representations from which to render athree-dimensional graphical object.

Computer 1702 may also include other removable/non-removable,volatile/non-volatile computer storage media. By way of example, FIG. 17illustrates a hard disk drive 1716 for reading from and writing to anon-removable, non-volatile magnetic media (not shown), a magnetic diskdrive 1718 for reading from and writing to a removable, non-volatilemagnetic disk 1720 (e.g., a “floppy disk”), and an optical disk drive1722 for reading from and/or writing to a removable, non-volatileoptical disk 1724 such as a CD-ROM, DVD-ROM, or other optical media. Thehard disk drive 1716, magnetic disk drive 1718, and optical disk drive1722 are each connected to the system bus 1708 by one or more data mediainterfaces 1726. Alternatively, the hard disk drive 1716, magnetic diskdrive 1718, and optical disk drive 1722 can be connected to the systembus 1708 by one or more interfaces (not shown).

The disk drives and their associated computer-readable media providenon-volatile storage of computer readable instructions, data structures,program modules, and other data for computer 1702. Although the exampleillustrates a hard disk 1716, a removable magnetic disk 1720, and aremovable optical disk 1724, it is to be appreciated that other types ofcomputer readable media which can store data that is accessible by acomputer, such as magnetic cassettes or other magnetic storage devices,flash memory cards, CD-ROM, digital versatile disks (DVD) or otheroptical storage, random access memories (RAM), read only memories (ROM),electrically erasable programmable read-only memory (EEPROM), and thelike, can also be utilized to implement the exemplary computing systemand environment.

Any number of program modules can be stored on the hard disk 1716,magnetic disk 1720, optical disk 1724, ROM 1712, and/or RAM 1710,including by way of example, an operating system 1726, one or moregraphics application programs 1728, other program modules 1730, andprogram data 1732. Each of such operating system 1726, one or moregraphics application programs 1728, other program modules 1730, andprogram data 1732 (or some combination thereof) may include anembodiment of program code to perform the macrostructure modeling withmicrostructure reflectance slices system and method.

A user can enter commands and information into computer 1702 via inputdevices such as a keyboard 1734 and a pointing device 1736 (e.g., a“mouse”). Other input devices 1738 (not shown specifically) may includea microphone, joystick, game pad, satellite dish, serial port, scanner,and/or the like. These and other input devices are connected to theprocessing unit 1704 via input/output interfaces 1740 that are coupledto the system bus 1708, but may be connected by other interface and busstructures, such as a parallel port, game port, or a universal serialbus (USB).

A monitor 1742 or other type of display device can also be connected tothe system bus 1708 via an interface, such as a videoadapter/accelerator 1744. Video adapter/accelerator 1744 is intended tohave a component thereof that represents 3-D commodity graphicshardware. As such, the 3-D commodity graphics hardware is coupled to thehigh-speed system bus 1706. The 3-D commodity graphics hardware may becoupled to the system bus 1708 by, for example, a cross bar switch orother bus connectivity logic. It is assumed that various otherperipheral devices, or other buses, may be connected to the high-speedsystem bus 1708, as is well known in the art. Further, the 3-D commoditygraphics hardware may be coupled through one or more other buses tosystem bus 1708.

In addition to the monitor 1742, other output peripheral devices caninclude components such as speakers (not shown) and a printer 1746 whichcan be connected to computer 1702 via the input/output interfaces 1740.

Computer 1702 can operate in a networked environment using logicalconnections to one or more remote computers, such as a remote computingdevice 1748. By way of example, the remote computing device 1748 can bea personal computer, portable computer, a server, a router, a networkcomputer, a peer device or other common network node, and the like.

The remote computing device 1748 is illustrated as a portable computerthat can include many or all of the elements and features describedherein relative to computer 1702. Logical connections between computer1702 and the remote computer 1748 are depicted as a local area network(LAN) 1750 and a general wide area network (WAN) 1752. Such networkingenvironments are commonplace in offices, enterprise-wide computernetworks, intranets, and the Internet.

When implemented in a LAN networking environment, the computer 1702 isconnected to a local network 1750 via a network interface or adapter1754. When implemented in a WAN networking environment, the computer1702 typically includes a modem 1756 or other means for establishingcommunications over the wide network 1752. The modem 1756, which can beinternal or external to computer 1702, can be connected to the systembus 1708 via the input/output interfaces 1740 or other appropriatemechanisms. It is to be appreciated that the illustrated networkconnections are exemplary and that other means of establishingcommunication link(s) between the computers 1702 and 1748 can beemployed.

In a networked environment, such as that illustrated with computingenvironment 1700, program modules depicted relative to the computer1702, or portions thereof, may be stored in a remote memory storagedevice. By way of example, remote application programs 1758 reside on amemory device of remote computer 1748. For purposes of illustration,application programs and other executable program components such as theoperating system are illustrated herein as discrete blocks, although itis recognized that such programs and components reside at various timesin different storage components of the computing device 1702, and areexecuted by the data processor(s) of the computer.

Computer-Executable Instructions

An implementation of the macrostructure modeling with microstructurereflectance slices system and method may be described in the generalcontext of computer-executable instructions, such as program modules,executed by one or more computers or other devices. Generally, programmodules include routines, programs, objects, components, datastructures, etc. that perform particular tasks or implement particularabstract data types. Typically, the functionality of the program modulesmay be combined or distributed as desired in various embodiments.

Exemplary Operating Environment

FIG. 17 illustrates an example of a suitable operating environment 1700in which an exemplary macrostructure modeling with microstructurereflectance slices system and method may be implemented. Specifically,the exemplary macrostructure modeling with microstructure reflectanceslices system and method described herein may be implemented (wholly orin part) by any program modules 1728-1730 and/or operating system 1726in FIG. 17 or a portion thereof.

The operating environment is only an example of a suitable operatingenvironment and is not intended to suggest any limitation as to thescope or use of functionality of the exemplary macrostructure modelingwith microstructure reflectance slices system and method describedherein. Other well known computing systems, environments, and/orconfigurations that are suitable for use include, but are not limitedto, personal computers (PCs), server computers, hand-held or laptopdevices, multiprocessor systems, microprocessor-based systems,programmable consumer electronics, wireless phones and equipments,general- and special-purpose appliances, application-specific integratedcircuits (ASICs), network PCs, minicomputers, mainframe computers,distributed computing environments that include any of the above systemsor devices, and the like.

Computer Readable Media

An implementation of an exemplary macrostructure modeling withmicrostructure reflectance slices system and method may be stored on ortransmitted across some form of computer readable media. Computerreadable media can be any available media that can be accessed by acomputer. By way of example, and not limitation, computer readable mediamay comprise “computer storage media” and “communications media.”

“Computer storage media” include volatile and non-volatile, removableand non-removable media implemented in any method or technology forstorage of information such as computer readable instructions, datastructures, program modules, or other data. Computer storage mediaincludes, but is not limited to, RAM, ROM, EEPROM, flash memory or othermemory technology, CD-ROM, digital versatile disks (DVD) or otheroptical storage, magnetic cassettes, magnetic tape, magnetic diskstorage or other magnetic storage devices, or any other medium which canbe used to store the desired information and which can be accessed by acomputer.

“Communication media” typically embodies computer readable instructions,data structures, program modules, or other data in a modulated datasignal, such as carrier wave or other transport mechanism. Communicationmedia also includes any information delivery media.

The term “modulated data signal” means a signal that has one or more ofits characteristics set or changed in such a manner as to encodeinformation in the signal. By way of example, and not limitation,communication media includes wired media such as a wired network ordirect-wired connection, and wireless media such as acoustic, RF,infrared, and other wireless media. Combinations of any of the above arealso included within the scope of computer readable media.

For purposes of the explanation, specific numbers, materials andconfigurations are set forth above in order to provide a thoroughunderstanding of the present invention. However, it will be apparent toone skilled in the art that the present invention may be practicedwithout the specific exemplary details. In other instances, well-knownfeatures are omitted or simplified to clarify the description of theexemplary implementations of present invention, and thereby betterexplain the present invention. Furthermore, for ease of understanding,certain method operations are delineated as separate operations;however, these separately delineated operations should not be construedas necessarily order dependent in their performance.

The inventors intend these exemplary implementations to be examples andnot to limit the scope of the present invention. Rather, the inventorshave contemplated that the present invention might also be embodied andimplemented in other ways, in conjunction with other present or futuretechnologies.

The present invention may be embodied in other specific forms withoutdeparting from its spirit or essential characteristics. The describedembodiments are to be considered in all respects only as illustrativeand not restrictive. The scope of the invention is, therefore, indicatedby the appended claims rather than by the foregoing description. Allchanges which come within the meaning and range of equivalency of theclaims are to be embraced within their scope.

1. A computer rendering method comprising: moving a semitransparentplane including a plurality of reflection points relative to an axis;and rendering an image of the plurality of reflection points at aplurality of positions with respect to the axis such that each saidpoint maps an elongated, continuous image.
 2. The computer renderingmethod as defined in claim 1, wherein moving the semitransparent planeincluding the plurality of reflection points relative to the axiscomprises rotating the plane about, and translating the plane withrespect to, the axis.
 3. The computer rendering method as defined inclaim 1, wherein moving the semitransparent plane including theplurality of the reflection points relative to the axis comprises movingthe plane of the reflection points perpendicular with respect to theaxis.
 4. The computer rendering method as defined in claim 3, whereinmoving the semitransparent plane including the plurality of thereflection points perpendicular with respect to the axis furthercomprising rotating the plane about, and translating the plane withrespect to, the axis.
 5. The computer rendering method as defined inclaim 1, wherein rendering the image comprises rendering a 3D model froma combination of images of the plurality of reflection points at aplurality of positions with respect to the axis.
 6. The computerrendering method as defined in claim 1, wherein: a plurality of controlpoints, each being located at an intersection of two axes, define athree-dimensional (3D) surface of a macrostructure; moving thesemitransparent plane including the plurality of reflection pointsrelative to the axis further comprises rotating and translating theplane of the reflection points respectively about and along each saidaxis of the 3D surface of the macrostructure; and rendering the image ofthe plurality of reflection points further comprises rendering a 3Dmodel from a plurality of images of a plurality of positions of theplanar plurality of reflection points with respect to each said axis ofthe 3D surface of the macrostructure.
 7. A computer-readable mediacomprising computer-executable instructions for performing the computerrendering method as recited in claim
 1. 8. A computer rendering methodcomprising: moving a plurality of voxels contained within parallelopposing planes with respect to an axis that is perpendicular to theparallel opposing planes, each said voxel being semitransparent andhaving a reflectance factor and a plurality of reflection points havinga density; and rendering an image of the plurality of voxels at aplurality of positions with respect to the axis such that at least onesaid point maps an elongated, continuous image.
 9. The method as definedin claim 8, wherein moving the plurality of voxels contained withinparallel opposing planes with respect to the axis comprises rotating theparallel opposing planes about, and translating the parallel opposingplanes with respect to, the axis.
 10. The method as defined in claim 8,wherein moving the plurality of voxels contained within parallelopposing planes with respect to the axis comprises moving the pluralityof voxels contained within parallel opposing planes perpendicular withrespect to the axis.
 11. The method as defined in claim 10, whereinmoving the plurality of voxels contained within parallel opposing planesperpendicular with respect to the axis further comprises rotating theplurality of voxels contained within parallel opposing planes about, andtranslating the plurality of voxels contained within parallel opposingplanes with respect to, the axis.
 12. The method as defined in claim 8,wherein: rendering the image comprises rendering a 3D model from acombination of images of the plurality of reflection points at aplurality of positions with respect to the axis; and the rendered imageaccounts for the interaction of each said reflectance factor of eachsaid voxel with respect to the other voxels of the plurality of voxelsat each said position of said plurality of positions.
 13. The method asdefined in claim 8, wherein: a plurality of control points, each beinglocated at an intersection of two axes, define a three-dimensional (3D)surface of a macrostructure; moving the planar plurality of reflectionpoints perpendicular relative to the axis further comprises rotating andtranslating the plane of the reflection points respectively about andalong each said axis of the 3D surface of the macrostructure; andrendering the image of the plurality of reflection points furthercomprises rendering a 3D model from a plurality of image of a pluralityof positions of the planar plurality of reflection points with respectto each said axis of the 3D surface of the macrostructure.
 14. Themethod as defined in claim 8, wherein each of the voxels has anassociated opacity and voxel reflectance function (VRF).
 15. The methodas defined in claim 14, wherein: the VRF represents the brightness of avoxel viewed from direction V(θ_(v),φ_(v)) when illuminated by a unitintensity light from direction L(θ_(l),φ_(l)); the VRF is represented bya four-dimensional color array after discretization of the four anglesθ_(l),φ_(l),θ_(v),φ_(v) θ is a longitude angle; and φ is an altitudeangle.
 16. The method as defined in claim 15, wherein: thediscretization of the four angles θ_(l),φ_(l),θ_(v),φ_(v) comprises thediscretization into directional increments; the directional incrementsfor the longitude angle are θ∈[0,2π]; and the directional increments ofthe altitude angle are φ_(l)∈[−π/2,π/2].
 17. A computer-readable mediacomprising computer-executable instructions for performing the renderingmethod as recited in claim
 8. 18. A machine-readable medium havinginstructions stored thereon for execution by a processor to perform amethod for rendering knitwear, the method comprising: generating aparameterized surface describing a three-dimensional (3D) knitwearmacrostructure; determining a plurality of control points that definethe parameterized surface, wherein each said control point is located atan intersection of two axes; applying a stitch pattern to each of thecontrol points of the knitwear skeleton to form a skeleton of the yarnstitches; discretizing the skeleton of the yarn stitches into aplurality of discretized yarn segments; sorting the discretized yarnsegments according to a viewing condition of a scene including theknitwear macrostructure and a distance of a view of the scene; inputtingthe plurality of discretized yarn segments into: a geometry of thescene; and a lighting condition of the scene; applying a lumislice, withrespect to a resolution of the distance of the view of the scene and asampling density, to each stitch of the stitch pattern of the sorteddiscretized yarn segments by translating and rotating the lumisliceperpendicular to and respectively along and about each stitch of thestitch pattern applied to the plurality of intersecting axes, whereinthe lumislice is semitransparent and is computed from a fiberdistribution of a yarn cross-section; and rendering a synthesis of thescene including the knitwear macrostructure using the sorted discretizedyarn segments having the lumislice applied thereto, the viewingcondition of the scene, and the distance of the view of the scene. 19.The medium of claim 18, wherein applying a stitch pattern to each of thecontrol points of the knitwear skeleton to form a skeleton of the yarnstitches further comprises applying a color pattern to each of thecontrol points of the knitwear skeleton to form the skeleton of the yarnstitches.
 20. The medium of claim 18, further comprising, beforeapplying the lumislice, computing a shadow map from the geometry of thescene and the lighting condition, wherein the synthesis of the scene isrendered using the computed shadow map.
 21. The medium of claim 18,wherein: each said lumislice characterizes attributions of across-sectional slice of yarn of the yarn stitches that is divided intovoxels; and each of the voxels has an associated opacity and voxelreflectance function (VRF).
 22. The medium as defined in claim 21,wherein: the VRF represents the brightness of a voxel viewed fromdirection V(θ_(v),φ_(v)) when illuminated by a unit intensity light fromdirection L(θ_(l),φ_(l)); the VRF is represented by a four-dimensionalcolor array after discretization of the four anglesθ_(l),φ_(l),θ_(v),φ_(v); θ is a longitude angle; and φ is an altitudeangle.
 23. The medium as defined in claim 22, wherein: thediscretization of the four angles θ_(l),φ_(l),θ_(v),φ_(v) comprises thediscretization into directional increments; the directional incrementsfor the longitude angle are θ∈[0,2π]; and the directional increments ofthe altitude angle are φ∈[−π/2,π/2].